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<li><a class="reference internal" href="#">Permutation Importance with Multicollinear or Correlated Features</a><ul>
<li><a class="reference internal" href="#random-forest-feature-importance-on-breast-cancer-data">Random Forest Feature Importance on Breast Cancer Data</a></li>
<li><a class="reference internal" href="#handling-multicollinear-features">Handling Multicollinear Features</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-inspection-plot-permutation-importance-multicollinear-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="permutation-importance-with-multicollinear-or-correlated-features">
<span id="sphx-glr-auto-examples-inspection-plot-permutation-importance-multicollinear-py"></span><h1>Permutation Importance with Multicollinear or Correlated Features<a class="headerlink" href="#permutation-importance-with-multicollinear-or-correlated-features" title="Permalink to this headline">¶</a></h1>
<p>In this example, we compute the permutation importance on the Wisconsin
breast cancer dataset using <a class="reference internal" href="../../modules/generated/sklearn.inspection.permutation_importance.html#sklearn.inspection.permutation_importance" title="sklearn.inspection.permutation_importance"><code class="xref py py-func docutils literal notranslate"><span class="pre">permutation_importance</span></code></a>.
The <a class="reference internal" href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">RandomForestClassifier</span></code></a> can easily get about 97%
accuracy on a test dataset. Because this dataset contains multicollinear
features, the permutation importance will show that none of the features are
important. One approach to handling multicollinearity is by performing
hierarchical clustering on the features’ Spearman rank-order correlations,
picking a threshold, and keeping a single feature from each cluster.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>See also
<a class="reference internal" href="plot_permutation_importance.html#sphx-glr-auto-examples-inspection-plot-permutation-importance-py"><span class="std std-ref">Permutation Importance vs Random Forest Feature Importance (MDI)</span></a></p>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>

<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">spearmanr</span>
<span class="kn">from</span> <span class="nn">scipy.cluster</span> <span class="kn">import</span> <span class="n">hierarchy</span>

<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.inspection</span> <span class="kn">import</span> <span class="n">permutation_importance</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
</pre></div>
</div>
<div class="section" id="random-forest-feature-importance-on-breast-cancer-data">
<h2>Random Forest Feature Importance on Breast Cancer Data<a class="headerlink" href="#random-forest-feature-importance-on-breast-cancer-data" title="Permalink to this headline">¶</a></h2>
<p>First, we train a random forest on the breast cancer dataset and evaluate
its accuracy on a test set:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">data</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">()</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">target</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>

<span class="n">clf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Accuracy on test data: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)))</span>
</pre></div>
</div>
<p>Next, we plot the tree based feature importance and the permutation
importance. The permutation importance plot shows that permuting a feature
drops the accuracy by at most <code class="docutils literal notranslate"><span class="pre">0.012</span></code>, which would suggest that none of the
features are important. This is in contradiction with the high test accuracy
computed above: some feature must be important. The permutation importance
is calculated on the training set to show how much the model relies on each
feature during training.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">result</span> <span class="o">=</span> <span class="n">permutation_importance</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">n_repeats</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
                                <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="n">perm_sorted_idx</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="n">importances_mean</span><span class="o">.</span><span class="n">argsort</span><span class="p">()</span>

<span class="n">tree_importance_sorted_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">feature_importances_</span><span class="p">)</span>
<span class="n">tree_indices</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">feature_importances_</span><span class="p">))</span> <span class="o">+</span> <span class="mf">0.5</span>

<span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">)</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="n">tree_indices</span><span class="p">,</span>
         <span class="n">clf</span><span class="o">.</span><span class="n">feature_importances_</span><span class="p">[</span><span class="n">tree_importance_sorted_idx</span><span class="p">],</span> <span class="n">height</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">feature_names</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">tree_indices</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">feature_importances_</span><span class="p">)))</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">boxplot</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">importances</span><span class="p">[</span><span class="n">perm_sorted_idx</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">vert</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
            <span class="n">labels</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">feature_names</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="handling-multicollinear-features">
<h2>Handling Multicollinear Features<a class="headerlink" href="#handling-multicollinear-features" title="Permalink to this headline">¶</a></h2>
<p>When features are collinear, permutating one feature will have little
effect on the models performance because it can get the same information
from a correlated feature. One way to handle multicollinear features is by
performing hierarchical clustering on the Spearman rank-order correlations,
picking a threshold, and keeping a single feature from each cluster. First,
we plot a heatmap of the correlated features:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">)</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">corr</span> <span class="o">=</span> <span class="n">spearmanr</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">correlation</span>
<span class="n">corr_linkage</span> <span class="o">=</span> <span class="n">hierarchy</span><span class="o">.</span><span class="n">ward</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
<span class="n">dendro</span> <span class="o">=</span> <span class="n">hierarchy</span><span class="o">.</span><span class="n">dendrogram</span><span class="p">(</span><span class="n">corr_linkage</span><span class="p">,</span> <span class="n">labels</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">feature_names</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">,</span>
                              <span class="n">leaf_rotation</span><span class="o">=</span><span class="mi">90</span><span class="p">)</span>
<span class="n">dendro_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">dendro</span><span class="p">[</span><span class="s1">&#39;ivl&#39;</span><span class="p">]))</span>

<span class="n">ax2</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">corr</span><span class="p">[</span><span class="n">dendro</span><span class="p">[</span><span class="s1">&#39;leaves&#39;</span><span class="p">],</span> <span class="p">:][:,</span> <span class="n">dendro</span><span class="p">[</span><span class="s1">&#39;leaves&#39;</span><span class="p">]])</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">dendro_idx</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">dendro_idx</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="n">dendro</span><span class="p">[</span><span class="s1">&#39;ivl&#39;</span><span class="p">],</span> <span class="n">rotation</span><span class="o">=</span><span class="s1">&#39;vertical&#39;</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">(</span><span class="n">dendro</span><span class="p">[</span><span class="s1">&#39;ivl&#39;</span><span class="p">])</span>
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>Next, we manually pick a threshold by visual inspection of the dendrogram
to group our features into clusters and choose a feature from each cluster to
keep, select those features from our dataset, and train a new random forest.
The test accuracy of the new random forest did not change much compared to
the random forest trained on the complete dataset.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">cluster_ids</span> <span class="o">=</span> <span class="n">hierarchy</span><span class="o">.</span><span class="n">fcluster</span><span class="p">(</span><span class="n">corr_linkage</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">criterion</span><span class="o">=</span><span class="s1">&#39;distance&#39;</span><span class="p">)</span>
<span class="n">cluster_id_to_feature_ids</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">cluster_id</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">cluster_ids</span><span class="p">):</span>
    <span class="n">cluster_id_to_feature_ids</span><span class="p">[</span><span class="n">cluster_id</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">selected_features</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">cluster_id_to_feature_ids</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>

<span class="n">X_train_sel</span> <span class="o">=</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="n">selected_features</span><span class="p">]</span>
<span class="n">X_test_sel</span> <span class="o">=</span> <span class="n">X_test</span><span class="p">[:,</span> <span class="n">selected_features</span><span class="p">]</span>

<span class="n">clf_sel</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="n">clf_sel</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_sel</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Accuracy on test data with features removed: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
      <span class="n">clf_sel</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test_sel</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)))</span>
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